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To make the gauge field theory foundation of the topological current of p-branes introduced in our previous work, we present a novel topological tensor current in SO( N) gauge field theory. This non-Abelian gauge field tensor current is the straightforward generalization of the Chern-Simons topological current of strings. By making use of the SO( N) gauge potential decomposition theory and the φ-mapping topological current theory, it is proved that the p-brane is created at every isolated zero of the Clifford vector field $\overrightarrow{\phi }(x)$ and the charges carried by p-branes are topologically quantized and labelled by the winding number of the φ-mapping. [ABSTRACT FROM AUTHOR]

Considering that gravitational force might deviate from Newton's inverse-square law and become much stronger in small scale, we present a method to detect the possible existence of extra dimensions in the ADD model. By making use of an effective variational wave function, we obtain the nonrelativistic ground energy of a helium atom and its isoelectronic sequence. Based on these results, we calculate gravity correction of the ADD model. Our calculation may provide a rough estimation about the magnitude of the corresponding frequencies which could be measured in later experiments. [ABSTRACT FROM AUTHOR]

In this paper, we first we present a general spherical symmetry solution, independent of any coordinate condition, to the Einstein equations. By using this solution, we obtain different cases in different coordinate conditions, such as Schwarzschild solution, Fock solution, which have different forms of f(r). Then, we obtain a modified formula with respect to f(r) of the Newtonian gravity. This formula may describe the gravity at small length scale. [ABSTRACT FROM AUTHOR]

We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are determined by the φmapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations. [ABSTRACT FROM AUTHOR]

In light of [lowercase_phi_synonym]-mapping topological current theory, the inner topological structure of Hopf invariant is investigated. It is revealed that Hopf invariant is just the winding number of Gauss mapping. According to the inner structure of topological current, a precise expression for Hopf invariant is also presented. It is the total sum of all the self-linking and all the linking numbers of the knot family. [ABSTRACT FROM AUTHOR]

Based on the Bogomol'nyi self-dual equation in the Abelian Chern–Simons Higgs model, we find a self-dual topological term which was ignored all the time in the Bogomol'nyi self-duality equation due to the improper decomposition of the complex Higgs field. We also present a generalized self-dual equation for the first time which unified the topological term and nontopological term in (2+1) space–time. It is shown that the self-dual vortex just arise from the symmetric phase of the Higgs field ϕ = 0, this provides a deep insight into the spontaneous symmetry breaking mechanism. When generalizing this model into (3+1) space–time, we show that the topological number on a family of knotted vortex are just the sum of linking number and self-linking number. We also find this topological charge is conserved during the splitting, the mergence and the intersection processes of knotted vortex lines. [ABSTRACT FROM AUTHOR]

In a previous paper, we addressed the method of Abelian decomposition to the case of SU(N) Yang–Mills theory. Here, we extend the decomposition method further to the general case. With the Cartan–Weyl basis we decompose semisimple group connection and discuss the SO(3,1) group in particular. In terms of the vierbein projection, we propose two two-forms as the U(1) gauge fields in the SO(3,1) gauge theory and show that these two-forms are just the different cosmic string tensors. Meanwhile, these two-forms indicate that the cosmic strings appear naturally in the Lorentz spacetime, i.e. the torsion in the Riemann–Cartan spacetime is not necessary for the cosmic strings. [ABSTRACT FROM AUTHOR]

We present a whole frame for the cosmic strings, inflation and dark energy with the complex scalar field which can be regarded as the order parameter of our universe. One can find that the comic strings emerge in the zeros of the complex scalar field in the early universe. And with the evolution of complex scalar field, inflation and dark energy can be understood in this frame. [ABSTRACT FROM AUTHOR]